If you use a Weather API that gets its information from the National Weather Service (NWS), information from that agency is within the public domain by federal law. Here are two that use data from NWS.
NOAA
Protocols: SOAP
Data Formats: XML, DWML
National Digital Forecast Database (NDFD) Extensible Markup Language (XML) is a service providing the public, government agencies, and commercial enterprises with data from the National Weather Service’s (NWS) digital forecast database.
Weather Underground
Protocols: REST
Data Formats: XML
Weather Underground provides real-time weather information via the Internet. Weather Underground provides weather reports for cities across the world as well as local weather reports for newspapers and Web sites.
At programmableweb.com you can search API's and Mashhups. Searching for weather API, I found 10.